Control System Design of Flywheel for Satellite Lin Xin Zhang ; Zheng Feng Bai 2 *; Yang Zhao ; Xi Bin Cao 3 Department of Astronautic Engineering, Harbin Institute of Technology, Harbin, 5000, P.R. China 2 Department of echanical Engineering, Harbin Institute of Technology, Weihai, 264209. P.R. China 3 Research Center of Spacecraft Technology, Harbin Institute of Technology, Harbin, 50080, P.R. China zhanglixin8377@sohu.com, baizhengfeng@26.com(*corresponding author),yangzhao@hit.edu.cn, xbcao@hit.edu.cn Abstract - Flywheel is an important executive component of satellite attitude control system. It has great significance to improve the performance of flywheel system for satellite attitude control system. For the momentum mode of flywheel, the system model and friction torque model of flywheel are established. And for the effects of flywheel friction torque and other interfering factors, close-loop control system of the flywheel speed is designed. Then the simulation is carried out and the results show that the output torque of flywheel has better precision when the close-loop control system is used. Besides, the viscous friction in flywheel friction torque is well depressed when using the control system of flywheel. The performance of flywheel system is improved and it has great significance for improving the attitude control system of satellite. Keywords - flywheel, friction model, feedback control, simulation INTRODUCTION Flywheel is an inertial actuator in a spacecraft attitude control system to generate suitable attitude control torques for correcting spacecraft attitude deviation or adjusting to an assigned attitude.flywheel control system is a key subsystem of the high precision attitude control system for satellite (Penne et al,2006; Silvestrin, 2005; Butz et al, 996). The accuracy and stability of attitude control system are affected directly by the performance of flywheel system. Therefore, improvement of the performance of flywheel control system has great significance for satellite attitude control system. With the development of attitude sensor and flywheel motor manufacturing technology, the effects of the performance of flywheel system on the stability and accuracy of the satellite attitude are more and more important. Flywheel is required to overcome periodic disturbing torque, achieve the instruction commands rapidly and not produce random disturbing torque for a high-accuracy and high-stability satellite. However, disturbances and noises usually exist in the flywheel (Hasha, 986; Valadi et al, 992; Xie, 200), especially the disturbance of friction torque inner the flywheel (Feeny et al, 998; Canudas et al, 995; Armstrong-Helouvry et al, 996). Those disturbances will cause errors of execution commands of flywheel and cause disturbance of the attitude control system of satellite. In order to improve the performance of flywheel attitude control system, the control system design of flywheel is necessary. So, the control system is used to the flywheel to decrease errors of execution commands in the design of flywheel system. In the presented work, the system model and friction torque model of flywheel are established for the momentum mode of flywheel. And then, according to the effects of flywheel friction torque and other interfering factors, the close-loop control system of flywheel speed is designed and analyzed. 2 FLYWHEEL SYSTE ODEL 2. omentum mode of flywheel The control torque is provided by flywheel in the attitude control system and there are two work modes for the different forms of flywheel control command (Goddu et al, 998; Weck, 998). One is torque mode (current mode), in which the input signal of the flywheel is torque command. Another is momentum mode (speed mode), the input signal of the flywheel is the desired control angular momentum. Desired value of the flywheel speed can be obtained by adjusting the voltage. Friction torque of the motor bearing is compensated by speed feedback in the momentum mode. For the momentum mode of flywheel, the accurate value of the flywheel speed is needed. However, the errors and noises of the speedometer will effects the accuracy of the output torque. In this paper, the control system of momentum mode of the flywheel is investigated and the schematic diagram is given in Fig.. As shown in Fig., flywheel system is presented in the dashed box, where K is circuit subdivision multiples, I R is motor armature resistance, L is motor armature inductance, K is motor torque coefficient, J is rotary inertia of motor shaft, K is motor back EF constant, e is motor electromagnetic torque, and c is d disturbing torque, respectively. In general case, the motor armature inductance is less and can be ignored. 0
Fig. Principle diagram of flywheel momentum mode According to the momentum mode of flywheel, the ATLAB/simulink model is designed and shown in Fig.2. In the actual situation, the saturation value of flywheel speed related to many factors, including wheel friction, voltage and current limitation of motor circuit, dynamic balance characteristic of flywheel and so on. In the case of these factors are not completely determined, speed saturation of the flywheel can be simulated by adding limitation module of the flywheel speed to the simulation model. When the saturation value of flywheel speed is reached, the output control torque of flywheel is switched to zero forcibly and the flywheel speed is constant. If direction of the input control torque is changed after the saturation value of flywheel speed reached, the output control torque of the flywheel is equal to the input control torque. Fig. 2 Simulink model of flywheel torque mode 2.2 Friction torque model of flywheel model Flywheel friction model is shown in Fig.3 and the formulas is presented as Eq.(). Fig. 3 Friction model of flywheel 0: Ff t Fcsgn t () u t, u t Fs 0: Ff t Fs, u t Fs (2) 02
where u t is external input force, Ff t is friction force, c is flywheel rotation angle, is flywheel angular velocity, and F is coulomb friction force, is viscous friction. Fv F s is static friction, Fig. 4 Simulink model of flywheel friction As shown in Fig.4, flywheel friction model is established by using the ATLAB/simulink. The input signals are flywheel angular velocity and motor electromagnetic torque. The output is friction torque, which includes static friction and dynamic friction. 3 DESIGN OF FLYWHEEL CONTROL SYSTE 3. Feed forward control of flywheel speed Due to the influences of motor shaft friction and other factors, it is not linear relationship between the flywheel angular momentum and input signal of the flywheel system. In order to decrease the error between the flywheel angular momentum and the input signal of angular momentum, it is necessary to control the flywheel system. The block diagram of the flywheel system is shown in Fig. 5. Fig. 5 Block diagram of flywheel system The transfer function between the input angular momentum and the flywheel angular speed can be obtained from Fig.5 and shown as: s KK G (3) H s J s K K K e KI KI where K. R Ls R For the ideal condition, the transfer function between the input angular momentum and the flywheel angular speed can be written as: s G0 (4) H s J Therefore, the feed forward control K can be added in the flywheel system and let: 03
KK G K s (5) J s K K K e J Then, the following result can be obtained. J s KK Ke s Ke K s (6) KK J KK J For the convenience of the attitude control system design, the input signal of the flywheel is torque signal, T. Hence, transfer function of the feed forward controller of flywheel is shown as: Ke K s J s K K (7) 3.2 Feedback control of flywheel speed If only open-loop control is used to the flywheel, the error between the flywheel speed and its desired value is existed inevitably due to the influences of flywheel friction torque and other interfering factors. In order to decrease such error, the close-loop control of flywheel speed is introduced and the proportional control method is used to control the speed. The control system is shown in Fig.6, where KP Ke J, KD KK and Kb is the feedback control coefficients. With the increase of feedback control coefficient, the error of flywheel speed is decreased. Due to the measurement error of flywheel angular speed is existed inevitably, take Kb 0 to prevent measurement error effect the control result. Fig. 6 Control system of flywheel speed 3.3 Simulation results of flywheel control In order to verify the effect of flywheel system, the square wave signal is added to the flywheel system. The output torque of the flywheel system is obtained. Fig.7 is the comparison curve between input torque signal of the flywheel, which is the expected output torque, and the real output torque signal. Fig. 8 is the error curve of flywheel output torque. The friction torque curve of the flywheel is shown in Fig. 9. As shown in Fig.7 and Fig.8, curves of the flywheel expected output torque and the real output torque are coincided, and the error is small. Therefore, the output torque of the flywheel system has good accuracy with the flywheel control system. The friction torque curve of the flywheel, as shown in Fig.9, shows that error between the expected output torque and the real output torque is mainly due to the sudden change of the friction torque direction. Besides, the viscous friction of the flywheel friction torque is well suppressed by the flywheel control system. In summary, the output torque of the flywheel system has good accuracy by the flywheel control system. Thus, performance of the flywheel system is improved, and it has great significance for the satellite attitude control system. 04
Fig. 7 Comparison between flywheel input torque and output torque Fig.8 Error of flywheel output torque Fig. 9 Friction torque curve of flywheel 05
4 CONCLUSION In this research, for the momentum mode (speed mode) of the flywheel system, close-loop control system of the flywheel speed is designed to overcome effects of the flywheel friction torque. The flywheel output torque shows high accuracy. The simulation results show that the output torque of the flywheel system is with good accuracy by the close-loop control system of the flywheel. eanwhile, viscous friction of the flywheel friction torque is well suppressed and the performance of the flywheel system is improved. It has positive significance for improving accuracy of the satellite attitude control system and also provides basis for control system design of the flywheel. ACKNOWLEDGENT This work is supported by Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT). The authors also would like to thank financial support provided by the Open Foundation of icro- Spacecraft Technology Key Laboratory. References Armstrong-Helouvry, B., and Amin, B. PID Control in the Presence of Static Friction, A Comparison of Algebraic and Escribing Function Analysis, Automatica, v.32, p.679-692, 996 Butz, P., and Renner, U. A mocrosat-bus for earth observation payloads, Proceedings of the 3rd International Symposium on Small Satellites Systems and Services, Annecy, France, 996 Canudas de Wit C.C., Olsson, H., Astrom, K.J., and Lischinsky, P. A New odel for Control of Systems with Friction, IEEE Transaction on Automatic Control, v.40, no.3, p.49-425, 995 Feeny, B., Guran, A., Hinrichs, N., and Popp, K., A Historical review on Dry Friction and Stick Slip Phenomena, American Society of echanical Engineers-Applied Echanics Review, v.5, p.32-34, 998 Goddu, Li.B.G., Chow,.Y., Detection of Common otor Bearing Faults Using Frequency-Domain Vibration Signals and a Neural Network Based Approach, Proceedings of the American Control Conference, June, p. 30-340, 998 Hasha,. D., Reaction Wheel echanical Noise Variations, Space Telescope Program Engineering emo SSS 28, June p. 75-83, 986 Penne, B.; Tobehn, C.; Kassebom,.; and Ziegler, B. A high agile satellite platform for earth observation-performance description using new generation missions, Proceedings of the 57th AIAA International Astronautical Congress, Valencia, Spain, 2006. Silvestrin P., Control and navigation aspects of the new earth observation missions of the European Space Agency, Journal of Annual Review in Control, v.29, p. 247-260, 2005 Valadi, S. R., and Oh. H. S., Space Station Attitude Control and omentum anagement: A Nonlinear Look, Journal of Guidance, Control and Dynamics. v.5, p.577-586, 992 Weck, D.O., Reaction Wheel Disturbance Analysis, IT SSL emo, October, 998:50-60 Xie, Y.C., Sawada, H., and Hashimoto, T., Actively controlled magnetic bearing momentum wheel and its application to satellite attitude control, Institute of Space and Astronautical Science, Report No. 680, 200 06